Self-adaptation Can Improve the Noise-tolerance of Evolutionary Algorithms

Real-world optimisation often involves uncertainty. Previous studies proved that evolutionary algorithms (EAs) can be robust to noise when using proper parameter settings, including the mutation rate. However, finding the appropriate mutation rate is challenging if the occurrence of noise (or noise level) is unknown. Self-adaptation is a parameter control mechanism which adjusts mutation rates by encoding mutation rates in the genomes of individuals and evolving them. It has been proven to be effective in optimising unknown-structure and multi-modal problems. Despite this, a rigorous study of self-adaptation in noisy optimisation is missing. This paper mathematically analyses the runtimes of 2-tournament EAs with self-adapting two mutation rates, fixed mutation rates and uniformly chosen mutation rate from two given rates on LeadingOnes with and without symmetric noise. Results show that using self-adaptation achieves the lowest runtime regardless of the presence of symmetric noise. In supplemental experiments, we extend analyses to other types of noise, i.e., one-bit and bit-wise noise. We also consider another self-adaptation mechanism, which adapts the mutation rate from a given interval. Self-adaptive EAs adapt their mutation rate to the noise level and outperform static EAs in these experiments. Overall, self-adaptation can improve the noise-tolerance of EAs in the noise-models studied here.